A novel approach for privacy homomorphism using attribute‐based encryption

Abstract

AbstractIn CRYPTO'13, Gentry et al. proposed the first homomorphic encryption (HE) scheme for the attribute‐based encryption (ABE). However, Gentry's scheme requires the same index for encryption of each ciphertext and supports only the key‐policy ABE. Indeed, in SECRYPT'13, Clear et al. left an open problem in the Gentry et al. scheme viz. a scheme that requires different sets of index in HE using ABE and supports the ciphertext‐policy ABE (CP‐ABE), where the sender is assumed to be intelligent. In addition, in INDOCRYPT'12, Vaikuntanathan discussed an open problem viz. to work out the HE using cryptographic techniques other than lattice‐based cryptography. With an aim to propose the CP‐ABE scheme using HE, in this research attempt, we propose an approach that integrates the benefits of HE in CP‐ABE and yet uses pairing‐based cryptography. In our approach viz. attribute‐based HE (AB‐HE), a user is able to successfully decrypt the ciphertext only if the attributes in the policy match those in the secret key. However, in addition, our approach also allows multiple invocations of multiplication operation on the ciphertext as in a typical partially HE, coupling the advantages of the partial HE in the CP‐ABE. Further, we also propose an extension of the proposed scheme that serves as a pseudo‐fully HE, but requires the help of a key authority. The security of the proposed scheme is based on the decisional bilinear Diffie–Hellman problem. To the best of our knowledge, ours is a unique attempt in integrating HE into the attribute‐based cryptography with different indexes/policies. In addition, our AB‐HE scheme is pairing‐based, and by adding more ciphertexts, it does not blow the final ciphertext size because we use the constant length ciphertext approach for the encryption. Copyright © 2016 John Wiley & Sons, Ltd.